Related papers: Quantitative Modelling of Diffusion-driven Pattern…
Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as…
This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species,…
Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [cond-mat/0312366] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
We examine a spatially discrete reaction diffusion model based on the interactions that create a periodic pattern in the Drosophila eye imaginal disc. This model is capable of generating a regular hexagonal pattern of gene expression behind…
MicroRNAs (miRNAs) are small RNA molecules, about 22 nucleotide long, which post-transcriptionally regulate their target messenger RNAs (mRNAs). They accomplish key roles in gene regulatory networks, ranging from signaling pathways to…
Recently, microRNAs (miRNAs) have emerged as central posttranscriptional regulators of gene expression. miRNAs regulate many key biological processes, including cell growth, death, development and differentiation. This discovery is…
Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which…
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
Theoretical descriptions of the stepping-stone model, a cornerstone of spatial population genetics, have long overlooked diffusive noise arising from migration dynamics. We derive an exact fluctuating hydrodynamic description of this model…
Humans excel at discovering regular structures from limited samples and applying inferred rules to novel settings. We investigate whether modern generative models can similarly learn underlying rules from finite samples and perform…